@@ -374,9 +374,9 @@ Instead of that, we implemented a~persistent version of both the \emph{primary}

which test extendability to the $n$- and $(n+1)$-skeleton of $X$.\footnote{The only exception is the case $n=3$, $\dim X>3$ where

the triviality of secondary obstruction is undecidable in general. However, if $X$ is assumed to be a triangulation of the cube $[0,1]^4$,

then our algorithm works with no essential changes. For many other fixed $4$-dimensional spaces $X$ the problem is decidable too.}

First, we compute the maximal $r_1$ for which the cohomological obstructions to extending

First, we compute the minimal $r_1$ for which the cohomological obstructions to extending

${f'}|_{A_{r_1}}$ to $A_{r_1}\cup X^{(n)}$ (\emph{primary obstruction}) vanishes.

Similarly, we compute a~maximal $r_2\geq r_1$ for which $f'|_{A_{r_2}}$ is extendable to $A_{r_2}\cup X^{(n+1)}$

Similarly, we compute a~minimal $r_2\geq r_1$ for which $f'|_{A_{r_2}}$ is extendable to $A_{r_2}\cup X^{(n+1)}$

(vanishing of the \emph{secondary obstruction}): this requires to parametrize all extensions to the $n$-skeleton.

%Via computational experiments with random Gaussian fields in low dimensions, we observe that

%the \emph{primary obstruction}, measuring non-extendability to the $n$-skeleton, is typically sufficient to detect a~robust zero of $f$.\footnote{This